P1112 Spring 2009
Homework #14 will not be collected.
Solutions
posted Friday May 1, and some of the HW will be
covered in section.
Reading: 13.3 – 13.8
(you may skip 13.4 molecules)
Problems:
1. Y&F 11.72
Lifting a bicycle wheel over a curb.
2.
Y&F 13.55
Physical pendulum.
3.
The position as a function of time
t
for a block of
mass
m
oscillating on a horizontal ideal spring of
spring constant
k
is
x
(
t
) =
A
cos(
ω
t
).
(a) Write the oscillator's velocity
v
(
t
) and acceleration
a
(
t
) in the form
C
cos(
ω
t
+
φ
), with
C
> 0, and find
the constants
C
and
φ
for each function. Your answers
should be in terms of
A,
ω
, and numerical constants.
(b) Write the oscillator's kinetic energy
K
(
t
) and
elastic potential energy
U
(
t
) as functions of time
t
that
are linear in sine or cosine of
t
. Your answers should
be in terms of
A,
ω
,
k, m,
and numerical constants.
[HINT:
The following trig identities will be useful:
sin
2
θ
= (1  cos2
θ
)/2
and
cos
2
θ
= (1 + cos2
θ
)/2.]
(c) For
two complete cycles
of this oscillation, draw
graphs showing the oscillator's position
x
(
t
), velocity
v
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 Spring '07
 LECLAIR,A
 Energy, Force, Work, 2 K, ωo, 0.050 kg

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